One popular approach to prepare graphene is to grow them on transition metal substrates via chemical vapor deposition. By using the density functional theory with dispersion correction, we systematically investigate for the first time the interfacial properties of bilayer (BLG) and trilayer graphene (TLG) on metal substrates. Three categories of interfacial structures are revealed. The adsorption of B(T)LG on Al, Ag, Cu, Au, and Pt substrates is a weak physisorption, but a band gap can be opened. The adsorption of B(T)LG on Ti, Ni, and Co substrates is a strong chemisorption, and a stacking-insensitive band gap is opened for the two uncontacted layers of TLG. The adsorption of B(T)LG on Pd substrate is a weaker chemisorption, with a band gap opened for the uncontacted layers. This fundamental study also helps for B(T)LG device study due to inevitable graphene/metal contact.
Graphene has become a ‘hot topic’ due to its extraordinary properties1,2,3 and wide range of possible applications4,5,6,7,8. Synthesis of high-quality graphene on a large scale is the foundation for its application. Among different preparation methods, growing graphene on transition metals including Cu9,10,11,12,13,14, Co15, Ni16,17, Pt18, Pd19, Au20, Ru21,22, Rh23, and Ir24,25 via chemical vapor deposition (CVD) is overwhelming because of high-quality, low preparation temperature, scalable production, and easy transfer to other substrates. Through CVD method, not only single layer graphene (SLG) but also few-layer graphene can be synthesized13,14,16. Among few-layer graphene, bilayer (BLG) and trilayer graphene (TLG) are the most extensively studied materials, partially due to the fact that there is an electrically tunable band gap in BLG26,27,28,29,30 and ABC-stacked TLG31,32,33,34 and meanwhile the carrier mobility is not degraded, which are critical for their application in transistor. Additionally, in an actual device, graphene has to be contacted with metal electrode. Therefore, the interfacial properties of B(T)LG and metal contacts should be clarified.
The interfacial properties between SLG and metals have been systematically studied23,35,36,37,38. The adsorption of SLG on Al, Ag, Cu, Au, and Pt (111) surfaces is a weak physisorption, which preserves the Dirac cone of SLG. By contrast, the adsorption of SLG on Ti (0001) surface, and Ni, Co, and Pd (111) surfaces is a strong chemisorption, which perturbs the electronic structure of SLG significantly. SLG is n-type doped by Al, Ag, Cu, Ti, Co, Ni and Pd, but p-type doped by Au and Pt. However, a systematic study on the interfacial properties between B(T)LG and metal substrates is lacking and leaves three fundamental issues open: (1) How do the B(T)LG/metal interfacial properties change with the species of metals? In view of the additional layer and easier break of inverse symmetry, new features may emerge when BLG and ABC-stacked TLG are contacted with metal substrates compared with SLG cases. (2) How do the TLG/metal interfacial properties depend on the stacking style of TLG? The second issue becomes especially crucial in light of the fact that the ABC- and ABA-stacked TLG possess inversion and mirror symmetries, respectively, resulting in a distinct response to electric field: A vertical electric field can open a band gap in ABC-stacked TLG but increase the overlap between the conduction and valence bands in ABA-stacked TLG instead31,32,33,34,39. (3) Previous theoretical studies have been reported that the contact effects between SLG and metal electrodes can affect the transport properties of SLG devices significantly40,41,42,43. For example, Al contacts can induce an extra conductance minimum at the Dirac point of the contacted region and giving rise to an electron-hole asymmetry40, and Ni and Co contacts can induce high spin polarization in graphene42. It is open how the metallic contacts affect the transport properties of B(T)LG devices.
In this Article, we provide the first systematic investigation on the interfacial properties of BLG and TLG on a variety of metals (Al, Ag, Cu, Au, Pt, Ti, Co, Ni, and Pd) by using the density functional theory (DFT) with dispersion correction (DFT-D) and establish the general physical picture of the B(T)LG/metal interfaces. Three categories of B(T)LG/metal interfacial structures are revealed in terms of the adsorption strength and electronic properties: The adsorption of B(T)LG on metal substrates (Al, Ag, Cu, Au, and Pt) is a weak physisorption in the first category of interfaces, but a band gap can be opened and its size depends on the possessed symmetries in graphene. The adsorption of B(T)LG on metal substrates (Ti, Ni, and Co) is a strong chemisorption in the second category of interfaces, and bands of the upper layer graphene of BLG are intact while a stacking-insensitive band gap is opened for the two uncontacted layers of TLG. The adsorption of B(T)LG on metal substrates (Pd) in the third category of interfaces is a weaker chemisorption, with a stacking-sensitive band gap opened for the two uncontacted layers of TLG and a band gap of 0.12 eV opened for the upper layer graphene of BLG. Finally, we design a two-probe model made of BLG contacted with Al and Ti electrodes, respectively, and calculate their transport properties by using ab initio quantum transport theory. Distinct transport properties are observed: A clear conductance gap rather than a conductance minimum appears at the Dirac point of the contacted region with Al as electrodes but this gap is full filled with Ti as electrodes.
Geometry and stability of B(T)LG on metal substrates
The most stable configurations of the SLG/metal interfaces are shown in Figure 1a (named after top-fcc interface, metal = Co, Ni, and Cu) and 1b (metal = Al, Ag, Pt, Au, and Ti)35,36. We choose the two configurations as the initial configuration of B(T)LG/metal contacts. After relaxation, the top view of the BLG/metal contacts keeps unchanged, as shown in Figure 1a and 1b, while the top view of the TLG/metal contacts favors split alignment of the first graphene layer with respect to metals, as shown in Figure 1c and 1d.
The calculated key data are presented in Table 1. The binding energy Eb of the B(T)LG/metal contact is defined as Where EG, EM, and EG/M are the relaxed energy for B(T)LG, the clean metal surface, and the combined system, respectively, and N is the number of interface carbon atoms in a unit cell. The interfacial distance dC-M is defined as the average distance of innermost graphene to metal surfaces. The B(T)LG/metal contacts can be classified into three categories according to the binding strength and the interfacial distance. In the first category of interfaces (Al, Ag, Cu, Au, and Pt (111) substrates), B(T)LG are physisorbed on these metal substrates with smaller binding energies of Eb = 0.096 − 0.153 eV and larger interfacial distances of dC-M = 3.13 − 3.53 Å; for TLG both quantities are insensitive to the stacking order. With larger Eb = 0.188 − 0.624 eV and smaller dC-M = 2.04 − 2.34 Å, B(T)LG are strongly chemisorbed on Ti (0001) surface, and Ni and Co (111) surfaces, forming the second category of interfaces. Differently, the binding in the second category of interfaces is always stronger by 0.06–0.09 eV for the ABC stacking style compared with the ABA stacking style. The adsorption of the third category of interfaces (Pd substrate) is a weak chemisorption (or strong physisorption), which is intermediate between the physisorption and strong chemisorption, with Eb = 0.166, 0.255, and 0.309 eV and dC-M = 2.70, 2.54, and 2.50 Å for BLG, ABA-, and ABC-stacked TLG, respectively. The same classification is applicable to the SLG/metal contacts35,36, and thus the graphene layer number has little effect on the adsorption categories. The flat planes of BLG and TLG are all kept in the first category of interfaces. But the innermost graphene layer buckles slightly with buckling heights of 0.01–0.11 Å in the second category of interfaces and 0.01–0.02 Å in the third category. The buckling height difference also reflects the difference of interaction strength among three categories of interfaces.
Electronic structure of BLG on metal substrates
The classification is also in accordance with the electronic structure of B(T)LG on metal surfaces. We calculate the band structures of the first category of interfacial structures. As shown in Figure 2, the band structure of the BLG can be clearly identified in these systems because of the weak interaction. Two important changes in the BLG bands are noteworthy: One is the Fermi level (Ef) of BLG is shifted upward or downward when contacted with the first class of metal surfaces, similar to SLG cases35,36. BLG is n-type (upward shift) doped when contacted with Ag, Al, and Cu but p-type doped (downward shift) when contacted with Au and Pt. This phenomenon can be attributed to the different work functions of BLG (WG, the calculated value is 4.58 eV) and metal surface (WM). The Fermi level shift is defined as ΔEf = Ef − ED, where ED is the middle energy of the band gap of the BLG adsorbed on metal substrates. Since the bands of the contacted and uncontacted layers are coupled together (Figure S1), the contacted and uncontacted layers share the same Fermi level shift, which reflects the total doping level of BLG but does not directly reflect the doping level of each layer (Figure S2b). Each layer has a different doping level, and the contact layer has a larger doping level than the uncontacted one. Taking BLG/Al contact as an example, the doping level of the contacted and uncontacted layer is 0.01 and 0 e per C atom, respectively, based on Mulliken charge analysis or 0.016 and 0.006 e per C atom, respectively, based on Bader charge analysis.
The Fermi level shift ΔEf as a function of (WM − WG) is plotted in Figure 3a. The change tendency of ΔEf with (WM − WG) is in accordance with that of the SLG cases35,36. The crossover point from n- to p-type doping is not at WM − WG = 0 but at about WM − WG = 0.4 eV (the LDA result for the SLG cases is WM − WG = 0.9 eV)35,36. At the crossover point, there is no charge transfer between metal and BLG. Therefore, the value of WM − WG at that point reflects the potential step resulting from the BLG-metal chemical interaction (Δc = 0.9 eV). Such a chemical interaction effectively reduces WM by Δc. As a result, a larger WM is needed to induce p-type doping in both BLG and SLG.
The other feature of the electronic structures of BLG in the first class of interfaces is the appearance of a band gap of Eg = 0.102–0.200 eV (Table 1), which is absent in their SLG counterparts. These band gaps are smaller than the maximum band gap of 0.25 eV opened in BLG under a vertical electric field29,44 and the maximum band gap of 0.34 eV opened in SLG sandwiched between hexagonal boron nitride under a vertical electric field45. The mechanism of band gap opening can be explained by a BLG/metal contact model, as shown in Figure 3b. We use Δn, Δn1, and Δn2 to denote the transferred electron density on metal surfaces, the bottom layer graphene, and the upper layer graphene, respectively. The electron transfer assumedly creates a uniform electric field E and E1 between the sheets. The potential difference between the two graphene sheets is where ε0 is the dielectric constant of vacuum. ΔU is thus proportional to the transferred electron density on the upper layer graphene. Due to ΔU ≠ 0, the inversion symmetry of A–B stacked BLG is broken. As a result, a band gap is induced, which has been confirmed by the tight-binding calculations in the system of depositing potassium on BLG46 and in few layer graphene under a vertical electric field32,47,48. The change of the band gap Eg as a function of ΔEf is shown in Figure 3c. Eg increases with the increasing |ΔEf| in both the n- and p-type doping regions. The cause lies in the fact with the increasing doping level in the n-type doping region (reflected by |ΔEf|), the more charge is transferred, and |Δn2| and |−αΔn2 − Δc| gets larger, leading to a larger |ΔU| and thus a larger Eg. The Eg − ΔEf data in the n-type doping region even can be roughly fitted by a linear function Eg = − 0.42 × ΔEf + 0.05 eV (black dashed line). It implies that there is a band gap of 0.05 eV for BLG physisorbed on metal substrates due to Δc even if the doping level is zero.
Experimentally, the current on/off ratio of a BLG field effect transistor (FET) is significantly improved by one order of magnitude when the channel BLG is deposited by Al, suggestive of opening of a transport gap in BLG49. This result is in agreement with our calculation that a band gap is opened for BLG on Al substrate. Furthermore, in terms of our calculations, the current on/off ratio of BLG FETs can also be improved by deposition of Cu, Ag, Au, and Pt on channel BLG.
The band structures of the second category of interfaces are shown in Figure 4. The 3d bands of Ti hybridize with both the π and π* bands of the bottom layer graphene because they are distributed widely both below and above the Dirac point. The hybridization between Ti and the bottom graphene is so strong that we even can't identify the π and π* bands of the bottom layer graphene, a result consist with the largest binding energy of BLG on Ti. Such a strong hybridization between Ti and SLG is also reported in previous theoretical works36,50. By contrast, the band structure of the upper layer graphene is almost intact and can be clearly identified, and the Dirac cone at the K point is well preserved. Unlike SLG, one is actually always able to observe the Dirac cone in the band structure of second category of interfaces. Therefore, we still can define the Fermi level shift as the difference between the Fermi level of the BLG/metal system and the identifiable Dirac cone (the middle energy of the band gap if a band gap is opened, see Table 1). Such a Fermi level shift is an observable quantum for example by angle-resolved photoemission spectroscopy (ARPES). Different from the first category of interfaces, the Fermi level shift in BLG/Ti interface belongs to the uncontacted layer (strictly it can be called ΔEf2 with a value of −0.283 eV) and reflects the doping level of the uncontacted layer. Because the Dirac cone of the contacted layer is completely destroyed, we can't determine its Fermi level shift from the band structure. They are two approximate schemes to estimate the Fermi level of the contacted layer strongly chemisorbed on metal36,50.
Kelly et al.36 estimate the Fermi level shift of SLG chemisorbed on Ti to be ΔEf = −0.31 eV by assuming that ΔEf is equal to the work function difference W − WG, while Chou et al.50 estimate ΔEf over −1 eV by assuming that the transferred electrons occupy the conduction band of SLG in a rigid band filling fashion. Actually, the precondition of ΔEf ≈ W − WG is that the position and shape of the Dirac cone of SLG is intact upon chemisorption on metal (see Figure S2a). Therefore, both methods to estimate ΔEf take the rigid band approximation and are at the same approximation level in this regard. It is difficult to judge which one is more proper because the accuracy of Kelly's scheme strongly depends on actual change of the position of the Dirac cone upon chemisorption, while Chou's scheme strongly depends on the charge analysis method. We also calculate the Fermi level shift of SLG adsorbed on Ti (0001) surface by using the two schemes but based on the same basis set (plane wave basis set) and functional (PBE-D) to eliminate the effect of the difference in the basis set and functional. Using Kelly' scheme, the resulting Fermi level shift of SLG is −0.58 eV, nearly twice the one given by Kelly et al (based on the LDA)36. On the other hand, the extra electron of SLG from the Mulliken and Bader charge analysis is 0.20 and 0.03 e per C atom, respectively (compared with the value of 0.1 e per C atom given by M. Y. Chou et al. from the Voronoi charge analysis50). Assuming a rigid band filling model, ΔEf is over −1 eV and −0.83 eV, respectively, both of which remain larger than that (−0.58 eV) estimated by using work function difference.
We can estimate the Fermi level shift of the contacted layer of BLG on Ti as ΔEf1 ≈ W − WG as we do for SLG if the shape and position of the Dirac cone of the contacted layer is assumed changed little. We have ΔEf1 ≈ W − WG = −0.69 eV. The higher doping level of the contacted layer than the uncontacted (ΔEf2 = −0.283 eV) is consistent with the requirement that the position of its Dirac cone of the uncontacted layer is higher than that of the contacted layer due to the built-in electric filed between them (see Figure S2c). Alternatively, ΔEf1 and ΔEf2 can also be estimated in terms of Chou's scheme. The excess electrons on the contacted and uncontaced layer we calculated are 0.20 and 0.01 e per C atom, respectively, from Mulliken population analysis. By using the rigid band filling model, ΔEf1 and ΔEf2 are estimated to be over −1 and −0.47 eV, respectively.
The majority spin bands of Ni and Co hybridize chiefly with the π bands of the bottom layer graphene, whereas the minority-spin bands of Ni and Co hybridize with both the π and π* bands of the bottom layer graphene, because most of the majority-spin 3d bands are below the Dirac point while some of the minority-spin 3d bands are above the Dirac point of graphene. Because the conduction bands of the contacted and uncontacted layers remained coupled together for the majority-spin, the Fermi level shifts (−0.428 and −0.364 eV for BLG/Co and BLG/Ni contacts, respectively) reflect the doping level of the whole BLG. By contrast, the conduction and valence bands of the contacted and uncontacted layers are completely decoupled for the minority-spin; therefore, for the minority-spin the Fermi level shift (−0.381 and −0.280 eV for BLG/Co and BLG/Ni contacts, respectively) determined from the band structure only reflects the doping level of the uncontacted layer. There are 0.14 (0.10) and 0.01 (0.01) extra electrons per carbon atom on the contacted and uncontacted layer from the Mulliken charge analysis when BLG on Co (Ni) substrate, resulting in an over −1 eV Fermi level shift for the contacted layer and −0.47 eV for the uncontacted layer according to a rigid band filling approximation. The latter value is comparable with the Fermi level shifts of the minority-spin determined from the band structure (−0.381 and −0.280 eV for BLG/Co and BLG/Ni contacts, respectively). However, the work function difference W − WG (−0.25 eV and −0.26 eV for BLG/Co and BLG/Ni contacts, respectively) appears to seriously underestimate the doping level of the contacted layer and not a good scheme herein. Our band structure of BLG on Ni (111) surface is in agreement with that reported by Gong et al51.
In Figure 4, we show the band structure of the third category of interfaces (BLG/Pd). The valence band of the contacted layer is completely destroyed due to the strong hybridization with the Pd 4d bands, while the conduction band of it remained coupled together with the one of the uncontacted layer, because most of the Pd 4d bands are below the Dirac point of BLG. The Fermi level shift is −0.160 eV, reflecting the doping level of the whole BLG. Similar to the second class of interfaces, the band structure of the upper layer graphene can be clearly identified, but a band gap of 0.124 eV is opened. This unique interfacial electronic structure of BLG/Pd is ascribed to the fact that the intermediate interaction between BLG and Pd surface preserves the partial electronic properties of the bottom layer and it does not overwhelm the intrinsic graphene interlayer coupling. The dipole field induced by Pd-graphene charge transfer breaks the inverse symmetry of the two graphene layers, and a band gap is opened. The Eg − ΔEf datum of BLG on Pd substrate falls in the Eg − ΔEf fitting curve for BLG physisorbed on metal substrates in the n-doping region (Figure 3c).
Electronic structure of TLG on metal substrates
The electronic structures of the first category of TLG/metal interfaces are plotted in Figure 5. It is clearly shown that the band structures of both ABA- and ABC-stacked TLG are preserved, accompanied by a Fermi level shift and an opened band gap. The same as BLG cases, TLG is doped with electrons by Al, Ag, and Cu contacts and with holes by Au and Pt contacts. We define the Fermi level shift of TLG as the difference between the Fermi level of the TLG/metal system and the identifiable Dirac cone (the middle energy of the band gap if a band gap is opened), ΔEf = ED − Ef. Table 1 summarizes the evolution of the Fermi-level shift ΔEf and band gap Eg of TLG. The Fermi-level shift ΔEf as a function of WM − WG is shown in Figure 6a for ABA- and ABC-stacked TLG (WG is the calculated work function of TLG, 4.52 eV). The crossover point from n- to p-type doping is about WM − WG = 0.56 for ABA-stacked TLG and 0.55 eV for ABC-stacked TLG.
Both the Fermi-level shift ΔEf and work function difference WM − WG are less sensitive to the stacking order. However, the stacking order affects significantly the band gap of TLG: ABA-stacked TLG has generally smaller band gaps of Eg = 0–0.061 eV while ABC-stacked TLG has generally larger band gaps of Eg = 0–0.249 eV. The current on/off ratio of TLG FET is expected to be increased by deposition of Al, Cu, and Ag on channel TLG due to a band gap opening. As shown in Figure 6b and Figure S3, the sizes of the band gap of both ABC- and ABA-stacked TLG rough linearly depend on ΔEf. The band gaps of ABC-stacked TLG are apparently electron-hole asymmetric: they are significantly larger in the n-type doping region (Eg = 0.181–0.249 eV) than those in the p-type doping region (Eg = 0–0.018 eV) at the same |ΔEf |. The band gaps of ABA-stacked TLG are slightly electron-hole asymmetric: the band gaps are slightly larger in the n-type doping region (Eg = 0.032–0.061 eV) than those in the p-type doping region (Eg = 0 eV) given the same |ΔEf| (Figure S3). The mechanism of band gap opening in ABA- and ABC-stacked TLG is also attributed to self-built electric field arising from charge imbalance between different layers. The detailed explanation to the mechanism and to the electron-hole asymmetry in the band gaps is provided in Supplementary Information in terms of a TLG/metal contact model (Figure S4).
The electronic structures of the second category of interfaces (TLG/Ti, Co, and Ni contacts) are plotted in Figure 7. Similar to BLG cases, both the π and π* states of the innermost graphene layer are strongly hybridized with the 3d states of Ti, and minority-spin 3d states of Co and Ni. Only the π states of the innermost graphene layer are strongly hybridized with the Co and Ni majority-spin 3d states. The strongly coupled innermost graphene layer serves as an active buffer and effectively passivates the metal d states at the interface. As a result, the electronic structure of the two uncontacted layers is nearly intact except that a band gap is opened, similar to the first category of interfaces for BLG/metal. The band gaps of the uncontaced BLG are less sensitive to the stacking mode, with Eg = 0.100–0.229 eV, which approach the maximum band gap of freestanding BLG obtained from the theoretical (0.25–0.28 eV)28,32 and experimental (0.25 eV)29 studies. The band gap opening is attributed to a potential energy difference between the two uncontacted graphene layers, which is ΔU32 = −αΔn3 − Δc′, where Δc′ is the potential step resulting from the interaction between the second graphene layer and the chemically bonded innermost graphene-metal system. Such a potential energy difference breaks the inversion symmetry of the two uncontacted graphene layers, thus opening a band gap. TLG is n-type doped in both stacking styles for the work function of the uncontaced BLG WG is larger than that of the new graphene-metal surface Wnew.
The electronic structures of the third category of interfaces (TLG/Pd contact) are shown in the second and fourth top panels of Figure 7. TLG is n-type doped by Pd substrate in both stacking styles. Though the π states of the innermost graphene layer are perturbed strongly, the π* states are only slightly affected, leading to BLG-like valence bands (two bands visible near the K point) and TLG-like conduction bands (three bands visible near the K point). The cause is the same as BLG cases: most of the Pd 4d states are below the Dirac point of graphene and they can only hybridize with the π states of the innermost graphene layer. Analogous to the physisorption cases, the band gap of the two uncontaced layers of TLG on Pd substrate is strongly dependent on the stacking mode, with Eg = 0.064 and 0.308 eV for ABA and ABC stacking styles, respectively. The latter band value is even marginally larger than the maximum band gap of freestanding BLG under a uniform electric field obtained from the theoretical (0.25–0.28 eV)28,32 and experimental (0.25 eV)29 studies and comparable with the maximum band gap of SLG sandwiched between h-BN sheet under a uniform electric field45. The unique behavior of TLG/Pd also agrees with the intermediate binding between typical physisorption and chemisorption.
Transport properties of BLG contacted with metal electrodes
Finally, we further study how the interfacial properties affect the transport properties of BLG devices when contacted with metallic Al and Ti leads. The two-probe model is presented in Figure 8a and the distance between the Al/Ti lead and BLG is 3.45/2.18 Å, according to our DFT results. The transmission spectrum of the device with Al electrodes is shown in Figure 8b, where a minimum (Dch) close to Ef due to the Dirac point of the channel BLG and a 0.22 eV gap at E − Ef = −0.6 eV are observed. By contrast, there are only one transmission minimum close to Ef for pure BLG without metal electrode (Inset in Figure 8b) and two transmission minima for SLG contacted with Al electrodes (one close to Ef, and the other at E − Ef = −0.6 eV due to the Dirac point of SLG in the lead) (Figure 8c). The transport gap in Figure 8b originates from a gap of the same size in the projected density of states (PDOS) of the BLG in the lead, as shown in Figure 8d, because the transmission coefficient of the device, T(E), is connected with the PDOS of the channel and the two electrodes via the relation52: where gch(E) and gL/R(E) are the PDOS of the channel and the left/right lead, respectively. Both gaps can be attributed to the band gap of Eg = 0.20 eV of corresponding infinite BLG contacted with Al electrodes. The transmission spectrum with Ti electrodes is shown in Figure 8e. Compared with Al contacts, the transmission minimum due to the Dirac point of the channel BLG remains but the transmission gap is absent because the characteristic conical point at the K point of the bottom layer graphene is destroyed. There is neither gap nor Dirac point in the PDOS of BLG in the lead (Figure S5). From the transmission spectra, Ti electrode can transport a larger current than Al electrode. In the light of similar interfacial properties of TLG/metals to BLG cases, the same contact effect on transport properties of TLG devices as BLG devices with Al and Ti electrodes is expected: Ti electrode can transport a larger current than Al electrode. The difference in the transport properties between Al and Ti electrodes in BLG is also reflected from a difference of the transmission eigenchannel at E − Ef = −0.6 eV and at the (π/3a, 0) point of the k-space. As displayed in Figure 8f, the transmission eigenvalue at this point nearly vanishes with Al electrodes, and the incoming wave function is nearly completely scattered and unable to reach to the other lead. By contrast, the transmission eigenvalue at the point is 0.96 with Ti electrodes, and the incoming wave function is scattered little and most of the incoming wave is able to reach to the other lead.
It has been established in prior work that that the generalized gradient approximation (GGA) yields a very small binding energy and a relatively large equilibrium distance for SLG/metal interface23. In order to better deal with graphene/metal interaction, which is a mixture of covalent, ionic, and van der Waals interactions, DFT-D, van der Waals density functional (vdW-DF), and random phase approximation (RPA) methods have been developed23,53,54,55,56,57. We show a comparison of the interface equilibrium distance and binding energy between SLG adsorbed on metal surfaces calculated by using local density approximation (LDA), GGA with Perdew–Burke–Ernzerhof (PBE) form58, vdW-DF, and RPA methods35,36,56 and BLG adsorbed on metal surfaces using DFT (PBE)-D method in Table 2 and 3, respectively. We can see that both PBE and vdW-DF give a large interface equilibrium distance, and LDA, DFT-D, and RPA give the similar and reasonable interface distances. The binding energies of DFT-D are close to those of RPA for Au and Pt cases. However, the binding energies of RPA for Ni and Co cases (chemisorption) seem too small, which are even smaller than Au adsorption (physisorption), and both LDA and DFT-D give large binding energies for Ni and Co cases. Therefore, DFT-D seems to be the most reliable method to describe graphene-metal interface, giving both the reasonable equilibrium distance and binding energy. The previous DFT-D calculation also gives a distance for graphene on Ir (111) surface that agrees well with the experimental data54. In DFT-D scheme, given the same geometry, DFT with and without dispersion gives the same band structure because the dispersion correction does not change electron density at all.
No band gap is detected experimentally for graphene on Pt18 and Au59. However, band gaps of 0.18, 0.25, and 0.32 eV are detected for graphene on Cu/Ni59, Cu60, and Ag/Ni59 substrates, respectively, in angle-resolved photoelectron spectroscopy (ARPES). If graphene is identified as single layer one, these measurements are apparently in contradiction with the calculated zero-gap for SLG on Cu and Ag substrates35,36,38. One possible solution to such a great discrepancy is to identify graphene as BLG or ABC-stacked TLG, since CVD growth on Ni substrate can yield few-layer graphene with random stacking order16,17 and on Cu substrate can yield bilayer12 and few-layer13,14 graphene, breaking the self-limiting nature of growth process. According to our calculations, BLG on Cu, and Ag (111) surfaces has a band gap of 0.11, 0.13 eV, and ABC-stacked TLG has a band gap of 0.181 and 0.203 eV, respectively, all of which are comparable with the measured values18,59,60.
Another interesting point is the different strength of interaction in different categories of interfaces. In terms of so-called d band model, the bond strength increases when moving to left and up in the transition metal series61. As moving from the right to the left, the d band moves up in energy, the filling of d band decreases and the antibonding graphene-metal d states become more depopulated, resulting in a strong bonding. Rises of the 3d, 4d, and 5d states are observed as going from Ni, Co, to Ti, from Ag to Pd, and from Au to Pt, respectively. From Table 1, we indeed have Eb (Ti) > Eb (Co) > Eb (Ni) > Eb (Cu) for 3d metals, Eb(Pd) > Eb(Ag) for 4d metals and Eb(Pt) > Eb(Au) for 5d metals. The same binding difference is available for SLG on metal substrate35,36. Because the Ni and Co 3d states of the minority-spin are higher in energy than those of the majority-spin (Figure 5), TLG should interact more strongly with the minority-spin states of Ni/Co in terms of this model.
As moving down in one group, relativistic effects become more remarkable in the core electrons, therefore the d-state orbitals of metals diffuse more widely, resulting in a worse overlapping of graphene π states and metal d states and a weaker binding23. Besides, the strength of covalent bond generally decreases with the increase of the atomic radius in one group. The calculated binding energy for group 10 metals (Ni, Pd, and Pt) with TLG indeed follows this rule and we have Eb (Ni) > Eb (Pd) > Eb (Pt) (See Table 1). In fact, Ti, Pd, and Pt are the three represents of the three classes of metals: BLG and TLG are strongly chemisorbed on Ni, and weakly chemisorbed on Pd, while the adsorption of graphene on Pt degenerates into a physisorption. The interaction strength change of graphene with group 9 metals Co, Rh, and Ir also obeys the same rule15,23,24,25.
Epitaxial ABA-stacked TLG on Ru (0001) surface has been investigated by Sutter et al.22. The electronic structure determined by selected-area APPES shows BLG-like π band dispersion. According to their DFT calculation, the two uncontacted graphene layers on Ru (0001) surface behave like freestanding BLG without a band gap though they are heavily n-type doped (the top of the valence band is located at −0.30 ± 0.05 eV below Ef). This result is somewhat surprising because the potential difference induced by graphene-metal electron redistribution will destroy the inversion symmetry of the two uncontacted graphene layers. We therefore recalculated the ABA-stacked TLG/Ru contact using the same parameters set by Sutter et al.22. The calculated electronic structure is shown in Figure S6. As expected, a band gap of 0.127 and 0.147 eV is opened in both the CASTEP and VASP calculations. The top of the valence band is located at −0.267 and −0.261 eV below Ef in the CASTEP and VASP calculations, respectively, consistent with the micro-ARPES data −0.30 ± 0.05 eV22. We note that the DFT calculation of Gong et al.51 for ABA-stacked TLG/Ni contact also found an energy gap of Eg = 0.133 eV for the majority-spin band, comparable with our value of 0.191 eV. This calculation also supports our results that the band gap of the uncontacted two layers is generally opened by the charge redistribution between metal and TLG in the second category of interfaces.
In summary, we present the first systematic first-principles investigation on the interfacial properties of BLG and TLG on a variety of metal substrates. According to the adsorption strength and electronic properties, the BLG/metal and TLG/metal interfacial structures can be classified into three categories. In the first category of interfaces, B(T)LG are physisorbed on Al, Ag, Cu, Au, and Pt substrates; a band gap of 0.1–0.2 eV is opened for BLG, and a stacking-sensitive band gap is opened for TLG, with the values of 0–0.061 and 0–0.249 eV for ABA- and ABC-stacking styles, respectively. In the second category of interfaces, B(T)LG are chemisorbed on Ti, Ni, and Co substrates; the bands of the bottom layer graphene are strongly perturbed, but those of the upper layer graphene of BLG are intact and a stacking-insensitive band gap is opened for the two uncontacted layers of TLG. In the third category of interfaces, B(T)LG are weakly chemisorbed on Pd substrate; a band gap of 0.12 eV is opened for the upper layer graphene of BLG and a band gap of 0.064 and 0.308 eV is opened for the two uncontacted layers of ABA- and ABC-stacked TLG, respectively. An ab initio quantum transport simulation is performed for a two-probe model made of BLG contacted with Al or Ti electrodes. A transmission minimum and a transport gap are observed in the transmission spectrum with Al contact. By contrast, there is only one transmission minimum in the transmission spectrum with Ti contact due to the strong binding in the electrodes. This fundamental study not only provides a deeper insight into the interaction between B(T)LG and metal substrates but also helps to B(T)LG-based device study because of inevitable B(T)LG/metal contact.
We use six layers of metal atoms (Ni, Co, Cu, Al, Ag, Cu, Pt, and Au) in (111) orientation and Ti in (0001) orientation to simulate the metal surface, and a hexagonal supercell is constructed with a BLG or TLG adsorbed on one side of the metal surface, as shown in Figure 1. We fix in-plane lattice constant of BLG or TLG to the experimental value a = 2.46 Å. The 1 × 1 unit cells of Ni, Co, and Cu (111) faces are adjusted to graphene 1 × 1 unit cell, and unit cells of Ti (0001) face and Al, Ag, Cu, Pt, and Au (111) faces are adjusted to graphene 2 × 2 unit cell. The approximation is reasonable since the metal surfaces have a small lattice constant mismatch of 0.8%, 1.6%, 4%, 1.6%, 2.2%, 2%, 1.2%, 3.2%, and 3.8% for Al, Ag, Cu, Au, Pt, Co, Ni, and Pd (111) and Ti (0001) faces with that of graphene, respectively. A vacuum buffer space of at least 12 Å is set.
The geometry optimizations and electronic structure calculations are performed with the ultrasoft pseudopotentials62 plane-wave basis set with energy cut-off of 350 eV, implemented in the CASTEP code63. GGA of PBE form58 to the exchange-correlation functional is used. To account for the dispersion interaction between graphene, a DFT-D semiempirical dispersion-correction approach is adopted64. During the calculations, the cell shape and the bottom four layers of metal atoms are fixed. To obtain reliable optimized structures, the maximum residual force is less than 0.01 eV/Å and energies are converged to within 5 × 10−6 eV per atom. The Monkhorst-Pack65 k-point mesh is sampled with a separation of about 0.02 and 0.01 Å−1 in the Brillouin zone, respectively, during the relaxation and electronic calculation periods. The component of the energy band and the plane-averaged excess electron density are analyzed via additional calculations based on the plane-wave basis set with a cut-off energy of 400 eV and the projector-augmented wave (PAW) pseudopotential implemented in the VASP code66,67. The electronic structures generated by the two packages are nearly indistinguishable.
TLG/Ru(0001) interface model is constructed from a slab of six layers of Ru with the bottom four layers are fixed and a TLG adsorbed on one side. Following the previous work by Sutter et al.22, ABA-stacked TLG is strained to match the Ru lattice parameter a = 2.68 Å. Using the same calculation parameters22, the ABA-stacked TLG/Ru contact is recalculated by using the CASTEP and VASP codes, respectively. Namely, ultrasoft pseudopotential62 plane-wave basis set with energy cutoff of 340 eV is used. The LDA in the Ceperley-Alder form is used for the exchange and correlation functional68,69. The Monkhorst-Pack65 k-point is sampled by a 15 × 15 mesh in the Brillouin zone.
To study how the metallic contacts affect the transport properties of the BLG devices, a two-probe model made of BLG is built, and the BLG channel is contacted with two Al/Ti electrodes (source and drain). We perform transport calculations at zero source-drain bias by using the DFT method coupled with nonequilibrium Green's function (NEGF) method, which are implemented in ATK 11.2 package70,71. Single-zeta (SZ) basis set is used, the real-space mesh cutoff is 150 Ry., and the temperature is set at 300 K. The LDA68,69 is employed for the exchange–correlation functional. The electronic structures of electrodes and central region are calculated with a Monkhorst–Pack65 50 × 1 × 100 and 50 × 1 × 1 k-point grid, respectively.
This work was supported by the National Natural Science Foundation of China (Nos. 11274016, 51072007, 91021017, 11047018, and 60890193), the National Basic Research Program of China (Nos. 2013CB932604 and 2012CB619304), Fundamental Research Funds for the Central Universities, National Foundation for Fostering Talents of Basic Science (No. J1030310/No. J1103205), Program for New Century Excellent Talents in University of MOE of China, and Nebraska Research Initiative (No. 4132050400) and DOE DE-EE0003174 in the United States. J. Zheng also acknowledges the financial support from the China Scholarship Council. J. Lu thanks Dr. Kritian S. Thygesen for helpful discussion.